Finite Group Databasebeta

← C37×#33552 #22654805

Subgroups — C37×#33552 #22654805

Order 9472.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3533C211yesmaximal, characteristic, complemented
2C37×#3026C211yesmaximal, characteristic, complemented
3C2×C37×#458C211yesmaximal, characteristic, complemented
4C37×#3019C211yesmaximal, characteristic, complemented
5C37×#2201C212yesmaximal, complemented
6C37×#2200C212yesmaximal, complemented
7C37×#2198C212yesmaximal, complemented
8C37×#2197C212yesmaximal, complemented
9C37×#2127C211yesmaximal, characteristic, complemented
10C37×#2121C211yesmaximal, characteristic, complemented
11C2×C37×#352C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C37C2211yescharacteristic
13C37×#575—21no—
14C37×#563C2211yescharacteristic, complemented
15C37×#562—21no—
16C37×#560C2211yescharacteristic, complemented
17C37×#559C2211yescharacteristic, complemented
18C37×#553—21no—
19C37×#552—21no—
20C37×#551—21no—
21C37×#551C2211yescharacteristic, complemented
22C37×#547—21no—
23C37×#546—21no—
24C37×#542—21no—
25C37×#540—21no—
26C37×#539—21no—
27C37×#538—21no—
28C37×#538—21no—
29C37×#535C2211yescharacteristic
30C37×#534—21no—
31C37×#534C2211yescharacteristic
32C37×#525—21no—
33C2×#123×C37—21no—
34C2×#123×C37C2211yescharacteristic
35C37×#458—21no—
36C37×#458—21no—
37C37×#458—21no—
38C37×#458C2212yes—
39C37×#458C2212yes—
40C37×#458C2212yes—
41C37×B(4,𝔽2)—21no—
42C37×B(4,𝔽2)C2212yes—
43C37×#455—21no—
44C37×#455C2212yes—
45C37×#453—21no—
46C37×#453C2212yes—
47C37×#421—21no—
48C2×#100×C37C2211yescharacteristic
49C2×#99×C37—21no—
50C2×#99×C37—21no—
51C2×#99×C37C2211yescharacteristic
52C2×#99×C37C2211yescharacteristic
53C37×#354C2212yescomplemented
54C37×#353C2212yescomplemented
55C37×#352C2212yescomplemented
56C37×#352C2212yescomplemented
57C37×#352C2212yescomplemented
58C37×AΣL(1,𝔽16)C2212yescomplemented
59H(5,𝔽2)×C37—21no—
60H(5,𝔽2)×C37—21no—
61H(5,𝔽2)×C37—21no—
62H(5,𝔽2)×C37—42no—
63H(5,𝔽2)×C37C2312yes—
64C2×#41×C37—21no—
65C2×#41×C37—21no—
66C2×#41×C37—41no—
67C2×#41×C37D411yescharacteristic, complemented
68C22×D4×C37—21no—
69C22×D4×C37—21no—
70C22×D4×C37—41no—
71C22×D4×C37D411yescharacteristic
72C22×D4×C37C2311yescharacteristic
73C23×C4×C37D411yescharacteristic, complemented
74#137×C37—22no—
75#137×C37—41no—
76AGL(1,ℤ/8)×C37—22no—
77AGL(1,ℤ/8)×C37—41no—
78#135×C37—42no—
79C2×M16×C37—21no—
80C4⋊Q8×C37—21no—
81#127×C37D411yescharacteristic, complemented
82#127×C37C2311yescharacteristic
83#126×C37—21no—
84#126×C37—21no—
85#126×C37—21no—
86#126×C37—21no—
87#126×C37—21no—
88#126×C37—21no—
89#125×C37—21no—
90#125×C37—21no—
91#125×C37—21no—
92#124×C37—21no—
93#124×C37—21no—
94#124×C37—21no—
95#124×C37—21no—
96#124×C37D411yescharacteristic, complemented
97#124×C37C2311yescharacteristic
98#123×C37—21no—
99#123×C37—21no—
100#123×C37—21no—
101#123×C37—21no—
102#123×C37—21no—
103#123×C37—21no—
104#123×C37—21no—
105#123×C37—21no—
106#123×C37—21no—
107#123×C37—21no—
108#123×C37—21no—
109#123×C37—21no—
110#123×C37—22no—
111#123×C37—22no—
112#123×C37—22no—
113#123×C37—41no—
114#123×C37—42no—
115#123×C37D411yescharacteristic
116#123×C37D411yescharacteristic, complemented
117#123×C37D411yescharacteristic, complemented
118#123×C37C2311yescharacteristic
119#123×C37C2311yescharacteristic
120#123×C37C2311yescharacteristic
121C22⋊Q8×C37—21no—
122C22⋊Q8×C37—21no—
123C22⋊Q8×C37—21no—
124C22⋊Q8×C37—21no—
125C22⋊Q8×C37—21no—
126C22⋊Q8×C37—21no—
127C22⋊Q8×C37—21no—
128C22⋊Q8×C37—21no—
129#121×C37—21no—
130#121×C37—21no—
131#121×C37—21no—
132#121×C37—21no—
133#121×C37—21no—
134#121×C37—21no—
135#121×C37—21no—
136#121×C37—21no—
137#121×C37—21no—
138#121×C37—21no—
139#121×C37—21no—
140#121×C37—21no—
141#121×C37—42no—
142#120×C37—21no—
143#120×C37—21no—
144#120×C37—21no—
145#120×C37—21no—
146#120×C37—22no—
147#120×C37—41no—
148#120×C37D411yescharacteristic
149#120×C37C2311yescharacteristic
150C4×Q8×C37—21no—
151C4×D4×C37—21no—
152C4×D4×C37—21no—
153C4×D4×C37—21no—
154C4×D4×C37—21no—
155C4×D4×C37—21no—
156C4×D4×C37—21no—
157C4×D4×C37—21no—
158C4×D4×C37—21no—
159C4×D4×C37—21no—
160#117×C37—21no—
161#117×C37—21no—
162#117×C37—21no—
163#117×C37D411yescharacteristic, complemented
164C2×C4⋊C4×C37—21no—
165C2×C4⋊C4×C37—21no—
166C2×C4⋊C4×C37—41no—
167C2×C22⋊C4×C37—21no—
168C2×C22⋊C4×C37—21no—
169C2×C22⋊C4×C37—21no—
170C2×C22⋊C4×C37—21no—
171C2×C22⋊C4×C37—41no—
172C2×C22⋊C4×C37D411yescharacteristic
173C2×C22⋊C4×C37D411yescharacteristic, complemented
174#104×C37—22no—
175#104×C37—22no—
176#100×C37—21no—
177#100×C37C2312yes—
178#99×C37—21no—
179#99×C37—21no—
180#99×C37—22no—
181#99×C37—22no—
182#99×C37—22no—
183#99×C37—22no—
184#99×C37C2312yes—
185#99×C37C2312yes—
186C24×C37—21no—
187C24×C37—21no—
188C24×C37C2×D411yescharacteristic
189C24×C37C2×D411yescharacteristic
190C24×C37C2×D411yescharacteristic
191#41×C37—22no—
192#41×C37—22no—
193#41×C37—42no—
194#41×C37—41no—
195#41×C37—42no—
196#41×C37—42no—
197#41×C37—41no—
198#41×C37—41no—
199#41×C37—42no—
200#41×C37—41no—
201#41×C37—81no—
202#41×C37—81no—
203C2×Q8×C37—21no—
204C2×Q8×C37—21no—
205C2×Q8×C37—21no—
206C2×Q8×C37C2×D411yescharacteristic
207C2×D4×C37—21no—
208C2×D4×C37—22no—
209C2×D4×C37—22no—
210C2×D4×C37—21no—
211C2×D4×C37—21no—
212C2×D4×C37—22no—
213C2×D4×C37—22no—
214C2×D4×C37—21no—
215C2×D4×C37—21no—
216C2×D4×C37—21no—
217C2×D4×C37—21no—
218C2×D4×C37—21no—
219C2×D4×C37—21no—
220C2×D4×C37—21no—
221C2×D4×C37—21no—
222C2×D4×C37—21no—
223C2×D4×C37—41no—
224C2×D4×C37—41no—
225C2×D4×C37—42no—
226C2×D4×C37—42no—
227C2×D4×C37—41no—
228C2×D4×C37—41no—
229C2×D4×C37—41no—
230C2×D4×C37—41no—
231C2×D4×C37—42no—
232C2×D4×C37—42no—
233C2×D4×C37—41no—
234C2×D4×C37—41no—
235C2×D4×C37—41no—
236C2×D4×C37—41no—
237C2×D4×C37—41no—
238C2×D4×C37—42no—
239C2×D4×C37C2×D411yescharacteristic
240C2×D4×C37C2×D411yescharacteristic
241C2×D4×C37C2×D411yescharacteristic
242C2×D4×C37C2×D411yescharacteristic
243C2×D4×C37C2411yescharacteristic
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—21no—
247C22×C4×C37—21no—
248C22×C4×C37—21no—
249C22×C4×C37—21no—
250C22×C4×C37—21no—
251C22×C4×C37—21no—
252C22×C4×C37—21no—
253C22×C4×C37—21no—
254C22×C4×C37—21no—
255C22×C4×C37—41no—
256C22×C4×C37—41no—
257C22×C4×C37—41no—
258C22×C4×C37—41no—
259C22×C4×C37—41no—
260C22×C4×C37C2×D411yescharacteristic
261C22×C4×C37C2×D411yescharacteristic
262C22×C4×C37C2×D411yescharacteristic
263C22×C4×C37C2×D411yescharacteristic
264Q16×C37—42no—
265SD16×C37—42no—
266SD16×C37—42no—
267D8×C37—42no—
268M16×C37—22no—
269M16×C37—41no—
270C2×C8×C37—41no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—21no—
281C4⋊C4×C37—21no—
282C4⋊C4×C37—21no—
283C4⋊C4×C37—21no—
284C4⋊C4×C37—21no—
285C4⋊C4×C37—21no—
286C4⋊C4×C37—21no—
287C4⋊C4×C37—21no—
288C4⋊C4×C37—21no—
289C4⋊C4×C37—21no—
290C4⋊C4×C37—42no—
291C4⋊C4×C37—42no—
292C4⋊C4×C37—42no—
293C22⋊C4×C37—21no—
294C22⋊C4×C37—21no—
295C22⋊C4×C37—21no—
296C22⋊C4×C37—21no—
297C22⋊C4×C37—21no—
298C22⋊C4×C37—21no—
299C22⋊C4×C37—21no—
300C22⋊C4×C37—21no—
301C22⋊C4×C37—21no—
302C22⋊C4×C37—21no—
303C22⋊C4×C37—21no—
304C22⋊C4×C37—21no—
305C22⋊C4×C37—21no—
306C22⋊C4×C37—21no—
307C22⋊C4×C37—21no—
308C22⋊C4×C37—21no—
309C22⋊C4×C37—21no—
310C22⋊C4×C37—21no—
311C22⋊C4×C37—21no—
312C22⋊C4×C37—21no—
313C22⋊C4×C37—21no—
314C22⋊C4×C37—21no—
315C22⋊C4×C37—21no—
316C22⋊C4×C37—22no—
317C22⋊C4×C37—22no—
318C22⋊C4×C37—42no—
319C22⋊C4×C37—41no—
320C22⋊C4×C37—41no—
321C22⋊C4×C37—42no—
322C22⋊C4×C37—42no—
323C22⋊C4×C37—42no—
324C22⋊C4×C37C2×D411yescharacteristic
325C22⋊C4×C37C2×D411yescharacteristic
326C22⋊C4×C37C2×D411yescharacteristic
327C22⋊C4×C37C2×D411yescharacteristic
328C42×C37—21no—
329C42×C37—21no—
330C42×C37—21no—
331C42×C37—21no—
332C42×C37C2×D411yescharacteristic
333C42×C37C2×D411yescharacteristic
334C23×C37—21no—
335C23×C37—21no—
336C23×C37—21no—
337C23×C37—21no—
338C23×C37—22no—
339C23×C37—22no—
340C23×C37—21no—
341C23×C37—21no—
342C23×C37—41no—
343C23×C37—41no—
344C23×C37—41no—
345C23×C37—41no—
346C23×C37—81no—
347C23×C37—81no—
348C23×C37—81no—
349C23×C37—82no—
350C23×C37—161no—
351C23×C37#12011yescharacteristic
352C23×C37#12011yescharacteristic
353C23×C37#12011yescharacteristic
354C23×C37C22×D411yescharacteristic
355C23×C37C22×D411yescharacteristic
356Q8×C37—22no—
357Q8×C37—41no—
358Q8×C37—41no—
359Q8×C37—81no—
360Q8×C37—81no—
361D4×C37—22no—
362D4×C37—41no—
363D4×C37—41no—
364D4×C37—41no—
365D4×C37—41no—
366D4×C37—41no—
367D4×C37—41no—
368D4×C37—42no—
369D4×C37—42no—
370D4×C37—42no—
371D4×C37—42no—
372D4×C37—42no—
373D4×C37—42no—
374D4×C37—41no—
375D4×C37—41no—
376D4×C37—41no—
377D4×C37—41no—
378D4×C37—81no—
379D4×C37—81no—
380D4×C37—81no—
381D4×C37—81no—
382D4×C37—81no—
383D4×C37—81no—
384D4×C37—81no—
385D4×C37—81no—
386D4×C37—81no—
387D4×C37—162no—
388C2×C4×C37—21no—
389C2×C4×C37—21no—
390C2×C4×C37—22no—
391C2×C4×C37—22no—
392C2×C4×C37—21no—
393C2×C4×C37—21no—
394C2×C4×C37—21no—
395C2×C4×C37—21no—
396C2×C4×C37—21no—
397C2×C4×C37—21no—
398C2×C4×C37—21no—
399C2×C4×C37—21no—
400C2×C4×C37—21no—
401C2×C4×C37—21no—
402C2×C4×C37—42no—
403C2×C4×C37—42no—
404C2×C4×C37—41no—
405C2×C4×C37—41no—
406C2×C4×C37—41no—
407C2×C4×C37—41no—
408C2×C4×C37—41no—
409C2×C4×C37—41no—
410C2×C4×C37—41no—
411C2×C4×C37—41no—
412C2×C4×C37—42no—
413C2×C4×C37—42no—
414C2×C4×C37—81no—
415C2×C4×C37—81no—
416C2×C4×C37—81no—
417C2×C4×C37—81no—
418C2×C4×C37—81no—
419C2×C4×C37—81no—
420C2×C4×C37—81no—
421C2×C4×C37—81no—
422C2×C4×C37—82no—
423C2×C4×C37—161no—
424C2×C4×C37#12011yescharacteristic
425C2×C4×C37C22×D411yescharacteristic
426C8×C37—42no—
427#33552C3711yesmaximal, characteristic, direct product factor, Sylow
428C22×C37—21no—
429C22×C37—21no—
430C22×C37—21no—
431C22×C37—21no—
432C22×C37—41no—
433C22×C37—41no—
434C22×C37—41no—
435C22×C37—41no—
436C22×C37—41no—
437C22×C37—42no—
438C22×C37—41no—
439C22×C37—41no—
440C22×C37—41no—
441C22×C37—41no—
442C22×C37—42no—
443C22×C37—41no—
444C22×C37—41no—
445C22×C37—81no—
446C22×C37—81no—
447C22×C37—81no—
448C22×C37—82no—
449C22×C37—82no—
450C22×C37—82no—
451C22×C37—82no—
452C22×C37—161no—
453C22×C37—161no—
454C22×C37B(4,𝔽2)11yescharacteristic
455C22×C37B(4,𝔽2)11yescharacteristic
456C22×C37C2×#12011yescharacteristic
457C4×C37—21no—
458C4×C37—21no—
459C4×C37—41no—
460C4×C37—41no—
461C4×C37—41no—
462C4×C37—41no—
463C4×C37—41no—
464C4×C37—41no—
465C4×C37—42no—
466C4×C37—41no—
467C4×C37—41no—
468C4×C37—41no—
469C4×C37—41no—
470C4×C37—82no—
471C4×C37—82no—
472#3533C2×C3711yescharacteristic, complemented
473#3026C2×C3711yescharacteristic, complemented
474C2×#458C2×C3711yescharacteristic, complemented
475#3019C2×C3711yescharacteristic, complemented
476#2201C2×C3712yescomplemented
477#2200C2×C3712yescomplemented
478#2198C2×C3712yescomplemented
479#2197C2×C3712yescomplemented
480#2127C2×C3711yescharacteristic, complemented
481#2121C2×C3711yescharacteristic, complemented
482C2×#352C2×C3711yescharacteristic, complemented
483C2×C37—21no—
484C2×C37—21no—
485C2×C37—21no—
486C2×C37—41no—
487C2×C37—41no—
488C2×C37—41no—
489C2×C37—41no—
490C2×C37—81no—
491C2×C37—81no—
492C2×C37—82no—
493C2×C37C2×B(4,𝔽2)11yescharacteristic
494C2×H(5,𝔽2)C22×C3711yescharacteristic
495#575—21no—
496#563C22×C3711yescharacteristic, complemented
497#562—21no—
498#560C22×C3711yescharacteristic, complemented
499#559C22×C3711yescharacteristic, complemented
500#553—21no—
501#552—21no—
502#551—21no—
503#551C22×C3711yescharacteristic, complemented
504#547—21no—
505#546—21no—
506#542—21no—
507#540—21no—
508#539—21no—
509#538—21no—
510#538—21no—
511#535C22×C3711yescharacteristic
512#534—21no—
513#534C22×C3711yescharacteristic
514#525—21no—
515C2×#123—21no—
516C2×#123C22×C3711yescharacteristic
517#458—21no—
518#458—21no—
519#458—21no—
520#458C22×C3712yes—
521#458C22×C3712yes—
522#458C22×C3712yes—
523B(4,𝔽2)—21no—
524B(4,𝔽2)C22×C3712yes—
525#455—21no—
526#455C22×C3712yes—
527#453—21no—
528#453C22×C3712yes—
529#421—21no—
530C2×#100C22×C3711yescharacteristic
531C2×#99—21no—
532C2×#99—21no—
533C2×#99C22×C3711yescharacteristic
534C2×#99C22×C3711yescharacteristic
535#354C22×C3712yescomplemented
536#353C22×C3712yescomplemented
537#352C22×C3712yescomplemented
538#352C22×C3712yescomplemented
539#352C22×C3712yescomplemented
540AΣL(1,𝔽16)C22×C3712yescomplemented
541C37#3355211yescharacteristic, direct product factor, Sylow
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C3712yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C3711yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C3711yescharacteristic
555C22×D4C23×C3711yescharacteristic
556C23×C4D4×C3711yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C3711yescharacteristic, complemented
565#127C23×C3711yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C3711yescharacteristic, complemented
580#124C23×C3711yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C3711yescharacteristic
599#123D4×C3711yescharacteristic, complemented
600#123D4×C3711yescharacteristic, complemented
601#123C23×C3711yescharacteristic
602#123C23×C3711yescharacteristic
603#123C23×C3711yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C3711yescharacteristic
632#120C23×C3711yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C3711yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C3711yescharacteristic
656C2×C22⋊C4D4×C3711yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C3712yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C3712yes—
668#99C23×C3712yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C3711yescharacteristic
672C24C2×D4×C3711yescharacteristic
673C24C2×D4×C3711yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C3711yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C3711yescharacteristic
723C2×D4C2×D4×C3711yescharacteristic
724C2×D4C2×D4×C3711yescharacteristic
725C2×D4C2×D4×C3711yescharacteristic
726C2×D4C24×C3711yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C3711yescharacteristic
744C22×C4C2×D4×C3711yescharacteristic
745C22×C4C2×D4×C3711yescharacteristic
746C22×C4C2×D4×C3711yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C3711yescharacteristic
808C22⋊C4C2×D4×C3711yescharacteristic
809C22⋊C4C2×D4×C3711yescharacteristic
810C22⋊C4C2×D4×C3711yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C3711yescharacteristic
816C42C2×D4×C3711yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C3711yescharacteristic
835C23#120×C3711yescharacteristic
836C23#120×C3711yescharacteristic
837C23C22×D4×C3711yescharacteristic
838C23C22×D4×C3711yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—41no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C3711yescharacteristic
908C2×C4C22×D4×C3711yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22C37×B(4,𝔽2)11yescharacteristic
937C22C37×B(4,𝔽2)11yescharacteristic
938C22C2×#120×C3711yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×C37×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C37C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C37
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C23×C37 ◁ C22×D4×C37 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C37×#3533C2semidirect
2. C37×#3026C2semidirect
3. C2×C37×#458C2semidirect
4. C37×#3019C2semidirect
5. C37×#2201C2semidirect
6. C37×#2200C2semidirect
7. C37×#2198C2semidirect
8. C37×#2197C2semidirect
9. C37×#2127C2semidirect
10. C37×#2121C2semidirect
11. C2×C37×#352C2semidirect
14. C37×#563C22semidirect
16. C37×#560C22semidirect
17. C37×#559C22semidirect
21. C37×#551C22semidirect
53. C37×#354C22semidirect
54. C37×#353C22semidirect
55. C37×#352C22semidirect
56. C37×#352C22semidirect
57. C37×#352C22semidirect
58. C37×AΣL(1,𝔽16)C22semidirect
67. C2×#41×C37D4semidirect
73. C23×C4×C37D4semidirect
81. #127×C37D4semidirect
96. #124×C37D4semidirect
116. #123×C37D4semidirect
117. #123×C37D4semidirect
163. #117×C37D4semidirect
173. C2×C22⋊C4×C37D4semidirect
427. #33552C37direct (N × H)
472. #3533C2×C37semidirect
473. #3026C2×C37semidirect
474. C2×#458C2×C37semidirect
475. #3019C2×C37semidirect
476. #2201C2×C37semidirect
477. #2200C2×C37semidirect
478. #2198C2×C37semidirect
479. #2197C2×C37semidirect
480. #2127C2×C37semidirect
481. #2121C2×C37semidirect
482. C2×#352C2×C37semidirect
496. #563C22×C37semidirect
498. #560C22×C37semidirect
499. #559C22×C37semidirect
503. #551C22×C37semidirect
535. #354C22×C37semidirect
536. #353C22×C37semidirect
537. #352C22×C37semidirect
538. #352C22×C37semidirect
539. #352C22×C37semidirect
540. AΣL(1,𝔽16)C22×C37semidirect
541. C37#33552direct (N × H)
550. C2×#41D4×C37semidirect
556. C23×C4D4×C37semidirect
564. #127D4×C37semidirect
579. #124D4×C37semidirect
599. #123D4×C37semidirect
600. #123D4×C37semidirect
646. #117D4×C37semidirect
656. C2×C22⋊C4D4×C37semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C37×#35332
C37×#30262
C2×C37×#4582
C37×#30192
C37×#22012
C37×#22002
C37×#21982
C37×#21972
C37×#21272
C37×#21212
C2×C37×#3522
#3355237